{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Create a list for each level of a binary tree.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is this a binary search tree?\n",
    "    * Yes\n",
    "* Should each level be a list of nodes?\n",
    "    * Yes\n",
    "* Can we assume we already have a Node class with an insert method?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* 5, 3, 8, 2, 4, 1, 7, 6, 9, 10, 11 -> [[5], [3, 8], [2, 4, 7, 9], [1, 6, 10], [11]]\n",
    "\n",
    "Note: Each number in the result is actually a node containing the number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We can use either a depth-first or a breadth-first search.  Intuitively, it seems like a breadth-first search might be a better fit as we are creating a linked list for each level.\n",
    "\n",
    "We can use a modified breadth-first search that keeps track of parents as we build the linked list for the current level.\n",
    "\n",
    "* Append the root to the current level's linked list `current`\n",
    "* While the `current` is not empty:\n",
    "    * Add `current` to `results`\n",
    "    * Set `parents` to `current` to prepare to go one level deeper\n",
    "    * Clear `current` so it can hold the next level\n",
    "    * For each `parent` in `parents`, add the children to `current`\n",
    "* Return the results\n",
    "    \n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run ../bst/bst.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BstLevelLists(Bst):\n",
    "\n",
    "    def create_level_lists(self):\n",
    "        if self.root is None:\n",
    "            return\n",
    "        results = []\n",
    "        current = []\n",
    "        parents = []\n",
    "        current.append(self.root)\n",
    "        while current:\n",
    "            results.append(current)\n",
    "            parents = list(current)\n",
    "            current = []\n",
    "            for parent in parents:\n",
    "                if parent.left is not None:\n",
    "                    current.append(parent.left)\n",
    "                if parent.right is not None:\n",
    "                    current.append(parent.right)\n",
    "        return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run ../utils/results.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_tree_level_lists.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_tree_level_lists.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestTreeLevelLists(unittest.TestCase):\n",
    "\n",
    "    def test_tree_level_lists(self):\n",
    "        bst = BstLevelLists(Node(5))\n",
    "        bst.insert(3)\n",
    "        bst.insert(8)\n",
    "        bst.insert(2)\n",
    "        bst.insert(4)\n",
    "        bst.insert(1)\n",
    "        bst.insert(7)\n",
    "        bst.insert(6)\n",
    "        bst.insert(9)\n",
    "        bst.insert(10)\n",
    "        bst.insert(11)\n",
    "\n",
    "        levels = bst.create_level_lists()\n",
    "        results_list = []\n",
    "        for level in levels:\n",
    "            results = Results()\n",
    "            for node in level:\n",
    "                results.add_result(node)\n",
    "            results_list.append(results)\n",
    "\n",
    "        self.assertEqual(str(results_list[0]), '[5]')\n",
    "        self.assertEqual(str(results_list[1]), '[3, 8]')\n",
    "        self.assertEqual(str(results_list[2]), '[2, 4, 7, 9]')\n",
    "        self.assertEqual(str(results_list[3]), '[1, 6, 10]')\n",
    "        self.assertEqual(str(results_list[4]), '[11]')\n",
    "\n",
    "        print('Success: test_tree_level_lists')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestTreeLevelLists()\n",
    "    test.test_tree_level_lists()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_tree_level_lists\n"
     ]
    }
   ],
   "source": [
    "%run -i test_tree_level_lists.py"
   ]
  }
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